How to examine differences between two groups across three different experimental conditions?

I have data for two groups. The 2 groups are matched on a number of variables, but differ in the scores on an alcohol measure (one group is high, and one is low). However the groups have been created so that they capture the extremes of the alcohol measure (all very low in one group, all very high in another) therefore the alcohol measure that separates them is not strictly continuous.

I then have data for the groups on task performance in 3 different conditions: reward, neutral, and punishment. I want to compare the groups for their task performance in each of these conditions, and additionally see if each group responds differently across the conditions.

I have conducted t-tests investigating if the means are different for each group, in each different condition. The groups significantly differ in one of the conditions.

Question 1: Would it be valid to do a RM-ANOVA treating each group as independent of each other, thus using a split file in SPSS and comparing scores across the three conditions within each group?

Question 2: I am considering a MANOVA, using task performance in the 3 conditions as dependent variables and group as the independent variable. If I were to do this, would it replace the t-tests or can it be used as additional examination (whereby I would have data using a univariate approach in the t-tests, and then using a multivariate approach using the MANOVA).

Any thoughts?

• I'm assuming that the dependent variable in each condition is numeric and is measured the same way in each condition? – Jeromy Anglim Oct 21 '11 at 1:44
• Yes, that is correct. – Short Elizabeth Oct 21 '11 at 7:47
• Please consider accepting some of the answers to your prior questions. – Andy W Oct 21 '11 at 12:32

Mixed ANOVA

I think a 2 (between subjects; alcohol group: low, high) by 3 (within subjects; condition; reward, neutral, punishment) mixed ANOVA would probably be a good way to analyse the data.

• The main effect of group would tell you overall whether the groups differ in mean performance averaged across the three conditions
• The main effect of condition would tell you whether overall performance varied across conditions.
• The group by condition interaction would tell you whether the effect of condition varied across groups.

Potential follow up tests

You could potentially perform follow up tests to further decompose the two main effects and interaction effects. You may wish to make performance of follow up tests conditional on the outcome of the initial main effect and interaction significance tests. Here are a few ideas:

• If the interaction effect is significant, perform analysis of simple effects, or interaction contrasts.
• If interaction effect is not significant or if performing analysis of simple effect of condition, and the condition effect is significant, then do some form of contrast or pair wise comparison of means to decompose effect of condition.

Alternatively, if you don't need statistical significance tests for all the little pairwise comparisons, you could just present a table or graph of the means (and some measure of error or variation) and comment on what you think the significance tests for the initial main and interaction tests mean. This is less rigorous, but sometimes sufficient.

Comments on the MANOVA Idea

I'm not a fan of the idea of running a MANOVA with group as IV and the three conditions as DVs. You wouldn't be testing the effect of condition or the interaction effect. If you truly don't care about such things, then the MANOVA would be a reasonable option; or you could simply create a composite variable (i.e., mean of the three conditions) and do an independent groups t-test on the composite.

• I am a novice at running a 2 x 3 ANOVA - can you let me know what assumptions I need to be aware of? I am guessing the usual ANOVA ones of homogeneity of variance, normality, excluded outliers is needed... are there any extras? – Short Elizabeth Oct 21 '11 at 2:27
• Here's an SPSS tutorial by Andy Field: statisticshell.com/docs/mixed.pdf ; sphericity and homogeneity of covariance are two assumptions to consider. – Jeromy Anglim Oct 21 '11 at 3:10